The Federal Migration Service confirmed he had completed the relevant paperwork at Moscow's Sheremetyevo airport, where he has been for the past three weeks.

Mr Snowden is wanted by the US for leaking details of government surveillance programmes.

He has no travel documents, so has been unable to take up asylum offers from a number of Latin American states.

"He reached the conclusion that he needs to write an application for temporary asylum, and this procedure has just been done," said Anatoly Kucherena, a lawyer with strong links with the Kremlin who helped Mr Snowden with the paperwork.

"For now he is not going to go anywhere. For now he plans to stay in Russia," he said.

Meanwhile the White House reiterated its position that the fugitive should be expelled and face trial in the US.

Analysis

By Daniel SandfordBBC News, Moscow

If there is a chance to grant Edward Snowden temporary asylum and then move him on to Latin America before September, that may be the best route for Russia.

But if that proves impossible, President Vladimir Putin will have to make a decision - does he continue to rub salt into America's wounds, or does he encourage Edward Snowden to leave quickly by making it clear that the asylum request is not going to work out.

What is still unclear is the extent to which the Russian intelligence agencies have been able to pump Edward Snowden for information, or even for the secret files themselves.

If they still want the information, there may be a trade-off involved - he gives the Russians what they desire and gets to leave the airport, and they decide that a poorer relationship with the US is the price they will have to pay for Mr Snowden's secrets.

"Mr Snowden should not be allowed to engage in further international travel except as necessary to return to the United States," spokesman Jay Carney said.

"He is not a human rights activist. He is not a dissident. He's accused of leaking classified information."

'Not Putin's decision'

Mr Kucherena said the fugitive had stated in the application that he faced possible torture and execution if he returned to the US.

If his application is accepted, he will be free to work and move freely in Russia, said the lawyer.

Russia's Interfax news agency quoted Mr Kucherena as saying he had asked Mr Snowden whether he would observe a request from President Vladimir Putin to not harm US interests if he is able to leave the airport.

Officials said Mr Snowden might be moved to an airport facility for accommodating refugees while his application was being processed, which should take no more than three months.

A presidential spokesman told Interfax that Mr Putin had not yet responded to the asylum request, and that the decision on whether it would be granted was not his to make.

But although the Russian government insists the decision will be made by a relatively junior official, the person in charge will be in no doubt what his boss would like him to do, says the BBC's Daniel Sandford in Moscow.

President Putin is clearly aware of the sensitivities involved, and the issue risks overshadowing talks with US President Barack Obama who is due to visit Russia in September, our correspondent adds.

Mr Snowden arrived in Russia on 23 June, having left Hong Kong, from where he had issued his leaks to the media.

He held a news conference at the airport on 12 July, where he said he was seeking asylum in Russia.

He has sent requests for political asylum to at least 21 countries, most of which have turned down his request. However, Bolivia, Nicaragua and Venezuela have indicated they could take him in.

But he is unable to leave the transit zone as he currently has no asylum documents or Russian visa, and the US has revoked his passport.

Some European countries are likely to close their airspace to any plane suspected of carrying the fugitive.

Meanwhile on Tuesday groups from across the political spectrum, including gun rights groups, churches and human rights groups filed a lawsuit demanding that the US National Security Agency hand over and destroy all the telephone communication data it has.

The lawsuit alleges the collection of phone records is an "illegal and unconstitutional programme of dragnet electronic surveillance". The US justice department has not commented on the case.

Mr Snowden's leaking of thousands of classified US intelligence documents has led to revelations that the National Security Agency is systematically seizing vast amounts of phone and web data.

The documents have also indicated that both the UK and French intelligence agencies allegedly run similarly vast data collection operations, and the US has been eavesdropping on official EU communications.